Tr. Morris, PROPERTIES OF DERIVATIVE EXPANSION APPROXIMATIONS TO THE RENORMALIZATION-GROUP, International journal of modern physics b, 12(12-13), 1998, pp. 1343-1354
Approximation only by derivative (or more generally momentum) expansio
ns, combined with reparametrization invariance, turns the continuous r
enormalization group into a set of partial differential equations whic
h at fixed points become nonlinear eigenvalue equations for the anomal
ous scaling dimension eta. We review how these equations provide a pow
erful and robust means of discovering and approximating non-perturbati
ve continuum limits. Gauge fields are briefly discussed. Particular em
phasis is placed on the role of reparametrization invariance, and the
convergence of the derivative expansion is addressed.